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Electric Fields

Using E = F/Q and E = V/d for point charges and uniform fields.

  • Define and explain Electric Fields in your own words
  • Use key terms such as field strength accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Electric Fields: using E = F/Q and E = V/d for point charges and uniform fields.

Definition: Electric Fields

Using E = F/Q and E = V/d for point charges and uniform fields.

Key ideas

Fields are mapped with lines

Field lines show direction — the way a test mass or positive charge would be pushed — and spacing shows strength: closer lines mean a stronger field. Gravitational and electric field lines radiate from masses and charges; magnetic field lines form closed loops, emerging from north poles and entering south poles.

Inverse-square laws govern point sources

Around a point mass, g = GM/r²; around a point charge, E = Q/(4πε₀r²). Doubling the distance quarters the field strength — the same mathematics in both cases, hinting at a deep unity. Inside a uniform field, like between charged plates, E = V/d is constant everywhere.

Key term — field strength: Force per unit mass (N/kg) or per unit charge (N/C) at a point in the field.

Worked example: Electric Fields

Describe the electric field pattern around an isolated positive point charge.

Radial lines pointing straight outwards from the charge, getting further apart with distance as the field weakens.

Answer: Radial lines pointing straight outwards from the charge, getting further apart with distance as the field weakens.

Common mistakes
  • Confusing electric potential with field strength Potential (V) is energy per unit charge; field strength (V/m) is its gradient — E = −ΔV/Δx.
  • Drawing field lines crossing Field lines never cross — a crossing would mean two field directions at one point, which is impossible.

Practice

Use Fleming's left-hand rule: magnetic field into the page, current to the right. Which way is the force?
First finger field, second finger current.

Upwards — with the first finger pointing into the page and the second finger to the right, the thumb points up.

A 0.3 m wire carrying 2 A sits perpendicular to a 0.5 T field. Find the force on it.
F = BIl.

0.5 × 2 × 0.3 = 0.3 N.

Why is no work done moving a charge along an equipotential?
What is the potential difference along it?

Potential is constant along an equipotential, so ΔV = 0 and W = QΔV = 0.

Earth's mass is 6.0 × 10²⁴ kg. Calculate g at 6.4 × 10⁶ m from its centre (G = 6.67 × 10⁻¹¹ N m²/kg²).
g = GM/r².

(6.67 × 10⁻¹¹ × 6.0 × 10²⁴) ÷ (6.4 × 10⁶)² = 4.0 × 10¹⁴ ÷ 4.096 × 10¹³ ≈ 9.8 N/kg.

Quick check

Electric Fields — quick check

Which of these best defines "field strength"?

Force per unit mass (N/kg) or per unit charge (N/C) at a point in the field.

A satellite orbits at twice Earth's radius from the centre. How does g there compare to the surface value?

g ∝ 1/r², so doubling r quarters g — about 9.8 ÷ 4 ≈ 2.45 N/kg.
Key takeaways
  • Electric Fields: using E = F/Q and E = V/d for point charges and uniform fields.
  • Fields are mapped with lines: Field lines show direction — the way a test mass or positive charge would be pushed — and spacing shows strength: closer lines mean a stronger field.
  • field: A region where an object experiences a non-contact force, mapped by field lines.
  • Watch out for: confusing electric potential with field strength
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